# Critical Window of The Symmetric Perceptron

@inproceedings{Altschuler2022CriticalWO, title={Critical Window of The Symmetric Perceptron}, author={Dylan J. Altschuler}, year={2022} }

We study the critical window of the symmetric binary perceptron, or equivalently, combinatorial discrepancy. Consider the problem of finding a binary vector σ satisfying ‖Aσ‖∞ ≤ K, where A is an αn×n matrix with iid Gaussian entries. For fixed K, at which densities α is this constraint satisfaction problem (CSP) satisfiable? A sharp threshold was recently established by Perkins and Xu [28], and Abbe, Li, and Sly [2], answering this to first order. Namely, for each K there exists an explicit…

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